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Factors and Multiples
Factors of a Number
A number may be
Factors of 24
made by multiplying
1
X
24
two or more other
Multiplication
2
X
12
combinations to
numbers together.
reach 24
3
X
8
The numbers that are
4X6
multiplied together
{1, factors
2, 3, 4,of6, 8, 12, 24}
are called
A list of its factors
the final number.
Greatest Common Factor
(GCF)
Greatest common
factor is the
greatest whole
number that is a
factor of two or
more given whole
numbers.
next page
What is the greatest common
factor of 36 and 48?
Factors of 36:
{1,
1 22, 3,
3 4,
4 6,
6 9
9, 12
12, 18
18, 36}
36
Factors of 48:
{1, 2, 3, 4, 6, 8,12, 16, 24, 48}
What is the greatest common
factor of 36 and 48?
Factors of 36:
{1,
1 2
2, 3
3, 4,
4 6
6, 9, 12
12, 18, 36}
Factors of 48:
{1,
1 2
2, 3
3, 4,
4 6
6, 8,12,
12 16, 24, 48}
Which
Whichfactors
is the greatest
are common
common
to both
numbers?
factor?
Greatest Common Factor
(GCF)
That was too much work. What
happened if we forgot to
include the 12 in one of the
factor list?
Want to learn a different way that’s easier?
Birthday Cake Method to find
GCF
Think of any number that divides
Divideinto
bothboth
numbers
evenly
36 andby482.
(a factor of both)
For this example, I’ll use 2.
18
2 36
24
48
Birthday Cake Method to find
GCF
Think of any number that divides
evenly
18 andby243.
Divideinto
bothboth
numbers
(a factor of both)
8 use 3.
For this6 example, I’ll
3 18
2 36
24
48
Birthday Cake Method to find
GCF
Continue
3 and 4 have
thisno
process
common
untilfactor
thereexcept
is no
other 1...
number
so you
besides
can stop
1 that
dividing.
is a factor
of 3both numbers.
4
2 6
3 18
2 36
8
24
48
Birthday Cake Method to find
GCF
The product of the numbers along the side
of
the
cake
is
the
GCF
2 xof336xand
2=
12
48.
3
2 6
3 18
2 36
4
8
24
48
Birthday Cake Method to find
GCF
Observe another example. Find the
GCF of 64 and 80.
8 x 2 = 16
4
8 32
2 64
no common
factor except 1
5
40
80
Multiples of a Number
The products of a number with the
natural numbers 1, 2, 3, 4, 5, ...
are called the multiples of the
number.
7x1=7
For example:
7 x 2 = 14
So, the multiples of 7 are 7 x 3 = 21
7
x
4
=
28
7, 14, 21, 28, and so on.
Multiples of a Number
Further examples:
multiples of 2 are 2, 4, 6, 8, …
multiples of 3 are 3, 6, 9, 12, …
multiples of 4 are 4, 8, 12, 16, …
Common Multiples
Multiples that are common to two or
more numbers are said to be common
multiples. For example:
6 8, 10, 12
Multiples of 2 are 2, 4, 6,
12, 14,
16, 18,
18 …
18 …
Multiples of 3 are 3, 66, 9, 12
12, 15, 18,
So, common multiples of 2 and 3 are 6,
12, 18, …
Example 2:
Find the common multiples of 4 and 6.
Solution:
12 16, 20, 24,
24
Multiples of 4 are 4, 8, 12,
28, 32, 36
36, …
Multiples of 6 are 6, 12
12, 18, 24
24, 30, 36
36,
…
So, the common multiples of 4 and 6
are 12, 24, 36, …
Least Common Multiple
(LCM)
The smallest common multiple
of two or more numbers is
called the least common
multiple (LCM).
Least Common Multiple (LCM)
To find the least common multiple
(LCM) of two or more numbers, list the
multiples of the larger number and stop
when you find a multiple of the other
number. This is the LCM.
Least Common Multiple (LCM)
Find the least common multiple of 6
and 9.
Solution:
List the multiples of 9 and stop when
you find a multiple of 6.
LCM is
18
Multiples of 9 are 9, 18, …
Multiples of 6 are 6, 12, 18, …
Birthday Cake Method to find
LCM
With the birthday cake method, you can
find both the GCF and LCM at the
same time!
Let’s use a previous example…
Birthday Cake Method to find
LCM
Find the least common multiple of
36 and 48.
Birthday Cake Method to find
LCM
Find the product of the
numbers
going
up and oncake!
Let’s make
the birthday
top of the cake.
3
2 6
x
3 18
x
2 36
x
x
= 144
4
8 144 is the
LCM
24 of 36 and
48
48
Birthday Cake Method to find
LCM
Another example: Find the LCM of 16
and 9.
Do 16 and 9 have any common factors
besides 1? No, they don’t. So their
LCM is their product…
?
16
X
9
= 144
Birthday Cake Method to find
LCM
Another example: Find the LCM of 5,
6 and 8.
Multiples
8 are 8,by16,
24, 32,
40, 48,
Finding
theofanswer
listing
multiples
56,the
64,largest
72, 80,number
88, 96,(8)
104, 112, 120, …
of
Stop ateventually
120 as it islead
a multiple
of both 5
would
you to the
answer of 120. and 6.
Birthday Cake Method to find
LCM
The birthday cake method can be used
to find the LCM of 5, 6 and 8. Watch!
5
2 5
x
x
3
6
x
4
8
= 120